Previous modifications to Stokes’s formula are based on either deterministic or stochastic considerations, with only one or the other being used exclusively in practice. This paper presents their band-limited combination, where stochastic modifications are used only in those parts of the gravity field spectrum where error variances are reliable, and deterministic modifications are used where they are not. This aims to optimise the filtering properties of the modified kernel such that the different components of the gravity field spectrum are weighted according to their known or perceived reliability. Because long-wavelength errors often occur in terrestrial gravity anomalies, the use of a low-degree spheroidal Stokes kernel is advocated so as to realise the full benefit of geoid models computed from the current and planned dedicated satellite gravity field missions. Deterministic kernel modifications appear to have gained a slightly wider acceptance in practical geoid computations, probably because estimates of the error degree variances of the terrestrial gravity data are either unavailable or unreliable, especially for the long wavelengths. In addition, the [global] error degree variances of global geopotential models are not necessarily representative of their errors in a particular region. This is because they use spherical harmonics, which are global basis functions (cf. Blais and Provins 2001). Examples of where no kernel modification (i.e., the spherical Stokes kernel) has been used to compute regional gravimetric geoid models include the USA (Smith and Roman 2001) and Canada (Fotopoulos et al. 1999), among many others. Examples of where deterministic kernel modifications have been used include Canada (Vanicek and Kleusberg 1987), South East Asia (Kadir et al. 1999) and Australia (Featherstone et al. 2001). Examples of where stochastic kernel modifications have been used include Europe (Denker and Torge 1998) and Sweden (Nahavandchi and Sjoberg 2001). Unfortunately however, the various types of Stokes’s kernel have not been used in the same region (using the same data) so as to allow their empirical comparison. As such, the type of kernel used appears to remain somewhat subjective.
The knowledge of sea level variations is of great importance in geoenvironmental and ocean-engineering applications. Estimations of sea level change with different warning times are of vital importance for the population of low-lying regions and islands. This contribution describes some recent advances in the application of a meshless artificial intelligence technique (neural networks) to the tasks of sea level retrieval and forecast. This technique was employed because it has been proven to approximate the non-linear behaviour in a geophysical system. The data used were taken from several SEAFRAME stations, which provide records for the Australian Baseline Sea Level Monitoring Project. A feed-forward, three-layered, artificial neural network was implemented to retrieve and predict sea level variations with different lead times. This methodology demonstrated reliable results in terms of the correlation coefficient (0.82-0.96), root mean square error (about 10% of tidal range) and scatter index (0.1-0.2), when compared with actual observations.
Abstract The rationale is given for a new determination of the Australian gravimetric geoid. In preparation for this task, the Australian Geological Survey Organisation’s gravity data base has been validated and reformatted. Additional information in the form of digital terrain data are available from the Australian Surveying and Land Information Group’s 9″ by 9″ Digital Elevation Model (DEM), derived from ∼5.2 million spot elevations and the ∼0.6 million elevations in the gravity data base. Both gravity and terrain data were transformed to give their horizontal position on the GRS80 ellipsoid, which produces a homogeneous data source for subsequent geoid computations. The gravity anomalies were computed using a second-order, free-air correction and normal gravity was computed using GRS80 latitude. Satellite altimeter-derived gravity anomalies are also considered as an additional source of information in offshore areas. The statistical fit of the new EGM96 global geopotential model to geometrical control provided by the Australian Fiducial and National GPS Networks is shown to be an improvement upon the OSU91A model, upon which AUSGEOID93 was based.
In regions where additional, spatially dense gravity and terrain information are available to augment existing data, a gravimetric determination of the geoid can be improved by incorporating these new data. In this study, 4,016 additional gravity observations, measured on a near-regular 2km by 3km grid in Western Australia have been used to compute a gravimetric geoid model using fast Fourier transform (FFT) techniques. A digital terrain model is also used during the geoid computations, which is derived from gravity station elevations and spot heights in the area. Using 21 spirit-levelled Australian Height Datum (AHD) heights in conjunction with Global Positioning System (GPS) ellipsoidal heights as control data, the standard deviation of the new gravimetric geoid is ±0.0824m. This represents a 31% improvement over the existing AUSGEOID93 gravimetric geoid and a 48% improvement over the OSU91A global geopotential model. Of these improvements, approximately 10% is due to the additional gravity data and approximately 1% is due to the terrain effects; the remainder is due to the dense gridding of the data prior to the FFT computations.
A new gravimetric determination of the geoid of the British Isles has been made, using a modified version of Stokes integral in combination with a global geopotential model and a digital terrain model.
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